Lottery balls are numbered and coloured balls. In the famous Lotto, six
numbered balls are drawn at random from 49 balls. In each ticket one needs
to guess the six numbers that would be drawn. If no correct guesses are
received the prize money is carried to the next draw. It is not uncommon to
see prize money accumulating to several millions of dollars. An urn contains m
white and n black balls. A ball is drawn at random and is put back into the
urn along with k additional balls of the same colour as that of the ball drawn.
A ball is again drawn at random. The probability of drawing a white ball now:

• p(w)=prob of geting white ball in first draw=m/(m+n)
  p(b)=n/(m+n)
  Now if first ball is drawn is White'k' white ball are added Total balls are m+n+k
  P(a/w)=P(getting white in 2nd / 1st ball drawn is'w')=(m+k)/(m+n+k)
  P(a2/w)=P(getting white in 2nd / 1st ball drawn is'b')=m/(m+n+k)
  so the p(w)=m/(m+n)*(m+k)/(m+n+k)+n/(m+n)*m/(m+n+k)
  p(w)=m(m+k)+mn/(m+n)(m+n+k)
  p(w)=m/m+n ans
• 9 years agoHelpfull: Yes(9) No(0)
• There are 2 conditions 1) if ball drawn first is white then total no of white balls= m+k. 2)if the ball drawn is black then there are m white and n+ k black.
  Total no of balls after first draw= m+n+k
  Prob.= (m+k)c1/(m+n+k)c1+mc1/(m+n+k)c1 =
  2m+k/m+n+k
  
• 9 years agoHelpfull: Yes(3) No(0)
• doesnt depend upon k
• 8 years agoHelpfull: Yes(3) No(0)
• prob= (1/2*mc1*1/2*(m-1)c1 + 1/2*nc1*1/2*mc1)/(1/2*mc1*1/2*(m-1)c1 + 1/2*mc1*1/2*nc1 + 1/2*nc1*1/2*n-1c1 + 1/2*mc1*1/2*nc1)
  ={m(m-1)+mn}/{m(m-1)+2mn+n(n-1)}
• 9 years agoHelpfull: Yes(2) No(0)